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Question

Find the sum of odd integers from 1 to 2001.

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Solution

The odd integers from1 to 2001 are 1,3,5,...1999,2001.

This sequence form an A.P.

Here, first term is, a=1 and common difference, d=2

Here a+(n1)d=2001

1+(n1)(2)=2001

2n2=2000

n=1001

Hence required sum is,

Sn=n2[2a+(n1)d]

=10012[2×1+(10011)×2]

=10012[2+1000×2]

=10012×2002

=1001×1001
=1002001

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